Problem 40 - Chemistry and Chemical Reactivity

Question

Which product, Ca or \(\mathrm{H}_{2}\), is more likely to form at the cathode in the electrolysis of \(\mathrm{CaCl}_{2} ?\) Explain your reasoning.

Step-by-Step Solution

Answer

Hydrogen gas ( \mathrm{H}_{2}\) is more likely to form at the cathode due to its higher reduction potential than calcium.

Step 1: Understanding Electrolysis Basics

In the process of electrolysis, an electric current is passed through a compound to cause a chemical change. Electrolysis involves the movement of cations and anions towards the cathode and anode, respectively. At the cathode, reduction occurs.

Step 2: Identify Possible Reductions at the Cathode

For the electrolysis of \(\mathrm{CaCl}_{2}\), the possible cation reductions are: \(Ca^{2+}\) to \(Ca\) and \(H^+\) (from \(H_2O\)) to \(H_2\). The reduction reactions are: \(Ca^{2+} + 2e^- \rightarrow Ca\) and \(2H^+ + 2e^- \rightarrow H_2\).

Step 3: Determine the Standard Reduction Potentials

The standard reduction potential for \(Ca^{2+} + 2e^- \rightarrow Ca\) is \(-2.87\, V\), and for \(2H^+ + 2e^- \rightarrow H_2\), it is \(0.00\, V\). The more positive the potential, the more likely the reduction will occur.

Step 4: Compare the Potentials

Since the standard reduction potential for \(2H^+ + 2e^- \rightarrow H_2\) is higher (\(0.00\, V\)) compared to \(Ca^{2+} + 2e^- \rightarrow Ca\) (\(-2.87\, V\)), \(H_2\) is more likely to be produced at the cathode under standard conditions.

Key Concepts

Reduction Potential

In electrochemistry, reduction potential is a measure of the tendency of a chemical species to acquire electrons and be reduced. The formula for a standard reduction potential is given in volts (V), and it indicates how readily a substance will undergo reduction under standard conditions, which include a solute concentration of 1 M, a pressure of 1 atm for gases, and a temperature of 25°C (298 K).
In our scenario with the electrolysis of \(\text{CaCl}_2\), we consider the reduction potential of \(\text{Ca}^{2+}\) to \(\text{Ca}\) which is \(-2.87 \, V\). On the other hand, the reduction potential for forming hydrogen gas \(\text{H}_2\) from ions in water is \(0.00 \, V\). This means that \(\text{H}_2\) is more likely to form as it has a higher (more positive) reduction potential. The rule of thumb here is: the more positive the potential, the greater the likelihood that the reduction reaction will occur at the cathode during electrolysis.

Cathode Reactions

The cathode in electrolysis is the electrode where reduction takes place. Reduction is the gain of electrons, so species at the cathode are transformed from a higher oxidation state to a lower one.
In the electrolysis of \(\text{CaCl}_2\), two possible reactions can occur at the cathode:

• \(\text{Ca}^{2+} + 2e^- \rightarrow \text{Ca}\)
• \(2\text{H}^+ + 2e^- \rightarrow \text{H}_2\)

These reactions involve the gain of electrons, resulting in the formation of an elemental state. During electrolysis, the preference of reaction depends heavily on the reduction potential. Since there's a greater tendency for \(\text{H}_2\) formation over calcium in their respective reduction potentials, hydrogen gas is favored to form at the cathode under typical conditions.

Chemical Change

The entire process of electrolysis is, in essence, a chemical change. A chemical change involves the rearrangement of atoms and altering of chemical bonds, leading to different substances being formed.
During electrolysis, electrical energy drives the non-spontaneous chemical reactions. When \(\text{CaCl}_2\) undergoes electrolysis, the electric current facilitates breaking apart the compound into calcium and chlorine ions.
From here:

• The \(\text{Ca}^{2+}\) ions migrate to the cathode, where they are reduced to form calcium metal if conditions favor it.
• Meanwhile, the chloride ions, \(\text{Cl}^{-}\), move to the anode to get oxidized into chlorine gas \(\text{Cl}_2\).

The end products, thus, are starkly different chemically from the initial compound, showcasing how impactful electrolysis is in prompting chemical change.

Standard Conditions

Standard conditions refer to a set of specific conditions agreed upon for measurements in chemistry to help maintain consistency. Typically, these include a pressure of 1 atmosphere, a temperature of 298 K (25°C), and solute concentrations at 1 Molarity. These conditions ensure that measurements like reduction potentials are comparable across different experiments and reactions.
In this exercise on \(\text{CaCl}_2\) electrolysis, considering the standard conditions helps us determine the products reliably using known data for reduction potentials. In any electrochemical cell, reactions are critically analyzed under these conditions to predict which processes are favored. Using these conditions as a baseline allows us to ascertain that \(\text{H}_2\) with a reduction potential of \(0.00\, V\) forms more readily than calcium at the cathode because it requires less energy input under these specific parameters.